Standard random-effects meta-analysis relies heavily on the assumption that the underlying true effects are normally distributed. In the social sciences, where evidence synthesis increasingly involves large, highly heterogeneous datasets, this assumption is often restrictive and unjustified. Misspecification of the random-effects distribution prevents the detection of asymmetry or multimodality, potentially leading to erroneous conclusions regarding the prevalence of adverse effects or the existence of specific subgroups. This paper introduces a Penalized Gaussian Mixture (PGM) framework designed to recover the entire probability density function of true effects without enforcing a rigid parametric shape. The method adapts to different non-normal scenarios, including skewed and multimodal distributions, while reducing to the normal case when supported by the data. A simulation study demonstrates that in large, highly heterogeneous meta-analyses, PGM yields substantially more accurate estimates of tail probabilities and the density function than standard methods when normality is violated, without substantially compromising efficiency under normality. An empirical application to environmental education data illustrates the practical utility of the method. The proposed framework provides researchers with a robust tool to move beyond simple summary statistics and characterize the complex nature of the true effect distribution in the real world.

翻译：标准随机效应元分析高度依赖真实效应服从正态分布的假设。在社会科学领域，当证据合成涉及大量高异质性数据集时，该假设往往具有限制性且缺乏合理性。随机效应分布的错误设定会阻碍非对称性或双峰性的检测，可能导致关于不良效应普遍性或特定亚组存在的错误结论。本文提出一种惩罚高斯混合（Penalized Gaussian Mixture, PGM）框架，能够在不强制设定参数形态的前提下恢复真实效应的完整概率密度函数。该方法可适应包括偏态分布与多峰分布在内的多种非正态场景，在数据支持时能自动退化为正态情形。模拟研究表明，在规模大、异质性高的元分析中，当正态性假设被违反时，PGM对尾部概率和密度函数的估计准确性显著优于标准方法，且在正态性成立时效率损失极小。通过环境教育数据的实证应用验证了该方法的实践价值。本框架为研究者提供了一种突破简单汇总统计量、刻画现实世界中真实效应分布复杂性的稳健工具。